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xiii, 541 p. ; 23 cm

xiii, 541 p. ; 23 cm

xiii, 541 p. ; 23 cm

xiii, 541 p. ; 23 cm

Computer Science Logic: 14th InternationalWorkshop, CSL 2000 Annual Conference of the EACSL Fischbachau, Germany, August 21 – 26, 2000 Proceedings Author: Peter G. Clote, Helmut Schwichtenberg Published by Springer Berlin Heidelberg ISBN: 978-3-540-67895-3 DOI: 10.1007/3-540-44622-2 Table of Contents: Background, Reserve, and Gandy Machines Choiceless Polynomial Time Computation and the Zero-One Law Composition and Submachine Concepts for Sequential ASMs Une tentative malheureuse de construire une structure éliminant rapidement les quanteurs Translating Theory into Practice — Abstract State Machines within Microsoft Choiceless Polynomial Time Logic: Inability to Express Schema Revisited Automated Verification = Graphs, Automata, and Logic A Fully Complete PER Model for ML Polymorphic Types Subtyping with Power Types The Descriptive Complexity of the Fixed-Points of Bounded Formulas Hypersequents and the Proof Theory of Intuitionistic Fuzzy Logic Continuous Functionals of Dependent Types and Equilogical Spaces Definability over Linear Constraints Bounded Arithmetic and Descriptive Complexity Independence: Logics and Concurrency Flatness Is Not a Weakness Sequents, Frames, and Completeness Disjunctive Tautologies as Synchronisation Schemes Axiomatizing the Least Fixed Point Operation and Binary Supremum

Machine Structures Professor Dan Garcia - Professor Michael Franklin Link to lecture notes http://inst.eecs.berkeley.edu/~cs61c/fa11/lec/11/

Machine Structures Professor Dan Garcia - Professor Michael Franklin Link to lecture notes http://inst.eecs.berkeley.edu/~cs61c/fa11/lec/11/

Machine Structures Professor Dan Garcia - Professor Michael Franklin Link to lecture notes http://inst.eecs.berkeley.edu/~cs61c/fa11/lec/11/

Preface (1985 Edition) - This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. - Philadelphia, July 1985 Jean Gallier

Preface (1985 Edition) - This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. - Philadelphia, July 1985 Jean Gallier

Preface (1985 Edition) - This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. - Philadelphia, July 1985 Jean Gallier

Preface (1985 Edition) - This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. - Philadelphia, July 1985 Jean Gallier

Preface (1985 Edition) - This book is intended as an introduction to mathematical logic, with an emphasis on proof theory and procedures for constructing formal proofs of formulae algorithmically. This book is designed primarily for computer scientists, and more generally, for mathematically inclined readers interested in the formalization of proofs, and the foundations of automatic theorem-proving. - Philadelphia, July 1985 Jean Gallier

In any case, notice that this quanti�ed phrase appears inside a larger if-then statement. This is quite normal; quanti�ed statements are themselves propositions and can be combined with and, or, implies, etc., just like any other proposition.

In any case, notice that this quanti�ed phrase appears inside a larger if-then statement. This is quite normal; quanti�ed statements are themselves propositions and can be combined with and, or, implies, etc., just like any other proposition.

In any case, notice that this quanti�ed phrase appears inside a larger if-then statement. This is quite normal; quanti�ed statements are themselves propositions and can be combined with and, or, implies, etc., just like any other proposition.

Logic and Grammar

In this paper I discuss what, according to my long experience, every computer scientist should know from logic. We concentrate on issues of modeling, interpretability and levels of abstraction. We discuss what the minimal toolbox of logic tools should look like for a computer scientist who is involved in designing and analyzing reliable systems. We shall conclude that many classical topics dear to logicians are less important than usually presented, and that less-known ideas from logic may be more useful for the working computer scientist.

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

1 online resource (500 pages)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

Foreword to the first edition by Edmund M. Clarke - FORE Systems Professor of Computer Science Carnegie Mellon University Pittsburgh, PA Formal methods have finally come of age! Specification languages, theorem provers, and model checkers are beginning to be used routinely in industry. Mathematical logic is basic to all of these techniques. (This foreword is re-printed in the second edition with its author’s permission.)

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

This volume constitutes the proceedings of the First International Workshop on Rewriting Logic, held at the Asilomar Conference Center, Pacific Grove, California, Sept. 2-6, 1996. The three invited papers by Narciso Marti-Oliet, Ugo Montanari, and Martin Wirsing, and seventeen contributed papers selected by the Program Committee give a rich view of the latest developments and research directions in the field of rewriting logic and its various applications to computing. Besides work on models and on concurrency aspects, there are several papers describing the different rewriting logic languages developed so far in Europe and the U.S., as well as a paper on semantic foundations for the Cafe language in Japan. There are also several papers on logical and metalogical specification; on reflection and strategies; on applications to object-oriented design, specification and programming; and on applications to contraint solving, to real-time systems, and to discrete event simulation. In addition to the papers, the workshop placed strong emphasis on facilitating in-depth discussion of the topics by allowing ample time for the discussion of each paper, and by including five panel discussions and a tutorial.

The Structure and Interpretation of Computer Programs

The Structure and Interpretation of Computer Programs

The Structure and Interpretation of Computer Programs

The Structure and Interpretation of Computer Programs

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.

In this paper we suggest that in the framework of the Category Theory it is possible to demonstrate the mathematical and logical \textit{dual equivalence} between the category of the $q$-deformed Hopf Coalgebras and the category of the $q$-deformed Hopf Algebras in QFT, interpreted as a thermal field theory. Each pair algebra-coalgebra characterizes, indeed, a QFT system and its mirroring thermal bath, respectively, so to model dissipative quantum systems persistently in far-from-equilibrium conditions, with an evident significance also for biological sciences. The $q$-deformed Hopf Coalgebras and the $q$-deformed Hopf Algebras constitute two dual categories because characterized by the same functor $T$, related with the Bogoliubov transform, and by its contravariant application $T^{op}$, respectively. The \textit{q}-deformation parameter, indeed, is related to the Bogoliubov angle, and it is effectively a thermal parameter. Therefore, the different values of $q$ identify univocally, and then label, the vacua appearing in the foliation process of the quantum vacuum. This means that, in the framework of Universal Coalgebra, as general theory of dynamic and computing systems ("labelled state-transition systems"), the so labelled infinitely many quantum vacua can be interpreted as the Final Coalgebra of an "Infinite State Black-Box Machine". All this opens the way to the possibility of designing a new class of universal quantum computing architectures based on this coalgebraic formulation of QFT, as its ability of naturally generating a Fibonacci progression demonstrates.